遗传密码的高维空间对称性

SYMMETRY OF GENETIC CODES IN HIGH DIMENSION SPACE

对称性是由均衡比例产生的匀称美。对称性和对称破缺在自然界和生命现象中普遍存在。20种氨基酸和终止码共有64个遗传密码子 ,组成一个6维的编码空间。遗传密码空间以对称轴将空间分成对称的两大部分 :嘌呤空间和嘧啶空间。遗传密码子的简并以对称轴为参考轴 ,呈平行排列。高简并度氨基酸 (6 ,4,3 ,简并度 )和低简并度氨基酸 (1 ,2简并度 )的简并子空间近似呈周期性的双交错方式排列。遗传密码的简并与4种核苷酸的二进制数字编码 ,具有密切的关系。经过分析 ,可得出遗传密码的连通性λλ简并法则 :“除丝氨酸的密码子分成两个与对称轴平行的 ,分离的子空间之外 ,其余氨基酸和终止密码的密码子 ,都通过与空间对称轴平行的λλ平面或λ边简并 ,组成独立的 ,单一的连通子空间。”并对氨基酸密码子的惯用率与编码空间的对称关系 ,以及数字生物学的意义进行了分析和讨论。

Symmetry,a beauty of uniformity owing to the harmonic proportion, is very common in natural world and life phenomena. 64 genetic condons of amino acids and terminate codes construct a graceful 6 dimension space. A symmetrical axis divides the genetic codon space into two symmetrical parts: the purine space and the pyrimidine space. All the degenerate subspaces of the genetic codons are in parallel with the symmetrical axis. The 4 nucleotides of DNA sequences can be further encoded with two-bit digits in which the first bit is the base bit to encode purines and pyrimidines and the second bit is the functional group bit to encode the keto group and amino group. The λλ degenerate rule of connectivity of the genetic codons can be derived as follows: 'except the codons of serine which are separated into two independent subspaces, all the codons of other 19 amino acids and terminate codes are degenerated through the λλ degeneracy to form the unique and independent subspaces of connectivity'. The relationship between the usage of genetic codons and the symmetry of genetic codon space is analyzed. The significance of the digital biology is also discussed.